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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Oct 2012 13:35:40 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/15/t13503225471zrrvh0qzm7qval.htm/, Retrieved Tue, 07 May 2024 08:05:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=177542, Retrieved Tue, 07 May 2024 08:05:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact37
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-15 17:35:40] [0dfc9291120e0017631158d00b067a5a] [Current]
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Dataseries X:
2048
2037
2149
2124
2205
2489
2573
2702
2718
2646
2712
2634
2614
2637
2649
2579
2505
2462
2467
2447
2656
2626
2483
2540
2503
2467
2513
2443
2293
2071
2030
2052
1864
1670
1811
1905
1863
2014
2198
2962
3047
3033
3504
3801
3858
3674
3721
3844
4117
4105
4435
4296
4203
4563
4621
4697
4591
4357
4503
4444
4291
4200
4139
3970
3862
3702
3570
3801
3896
3918
3813
3667




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=177542&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=177542&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=177542&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3091.72222222222106.10586001640529.1380911642789
Geometric Mean2963.34985769817
Harmonic Mean2840.34310390148
Quadratic Mean3218.39967996518
Winsorized Mean ( 1 / 24 )3092.625105.53341377555329.3046997093959
Winsorized Mean ( 2 / 24 )3093.23611111111105.12222093977729.4251404075946
Winsorized Mean ( 3 / 24 )3092.11111111111104.88306805119929.4815089657913
Winsorized Mean ( 4 / 24 )3091.05555555556103.86367933277629.7606976318632
Winsorized Mean ( 5 / 24 )3094.52777777778101.91498952977330.363813920363
Winsorized Mean ( 6 / 24 )3095.11111111111101.57737276907730.4704780871567
Winsorized Mean ( 7 / 24 )3088.20833333333100.09520690338430.8527094240805
Winsorized Mean ( 8 / 24 )3082.6527777777898.722816546802331.2253325584199
Winsorized Mean ( 9 / 24 )3082.5277777777898.541017595500531.281671866138
Winsorized Mean ( 10 / 24 )3072.9444444444496.084477797338331.9816948053348
Winsorized Mean ( 11 / 24 )3080.5833333333394.838518447818232.4824067662795
Winsorized Mean ( 12 / 24 )3074.5833333333392.580668944052933.2097766024063
Winsorized Mean ( 13 / 24 )3079.4583333333390.710579364948233.9481718107434
Winsorized Mean ( 14 / 24 )3078.4861111111190.149504135489534.1486749220975
Winsorized Mean ( 15 / 24 )3068.6944444444483.291220905948336.8429518869652
Winsorized Mean ( 16 / 24 )3090.4722222222277.381516204874139.938119253698
Winsorized Mean ( 17 / 24 )3086.2222222222276.491804623621840.3470964949512
Winsorized Mean ( 18 / 24 )3081.4722222222274.793897751969141.199513795109
Winsorized Mean ( 19 / 24 )3081.7361111111174.485207680231941.373800343568
Winsorized Mean ( 20 / 24 )3077.8472222222273.91592011977341.6398418261572
Winsorized Mean ( 21 / 24 )3073.4722222222272.061492857320142.6506876329584
Winsorized Mean ( 22 / 24 )3071.6388888888971.321168244303343.0677029625665
Winsorized Mean ( 23 / 24 )3076.1111111111170.808964478590943.442396506747
Winsorized Mean ( 24 / 24 )3050.1111111111166.926630919789345.5739526880807
Trimmed Mean ( 1 / 24 )3089.1104.70754133896229.5021730096772
Trimmed Mean ( 2 / 24 )3085.36764705882103.67830917304529.7590467250886
Trimmed Mean ( 3 / 24 )3081.07575757576102.65813388376530.0129725820296
Trimmed Mean ( 4 / 24 )3076.9375101.49248563503130.3168996280644
Trimmed Mean ( 5 / 24 )3072.83870967742100.40161076645830.6054722251924
Trimmed Mean ( 6 / 24 )3067.6333333333399.605918319236730.7977014327761
Trimmed Mean ( 7 / 24 )3061.9482758620798.649824705094731.0385576965342
Trimmed Mean ( 8 / 24 )3057.12597.774439142729531.267118756235
Trimmed Mean ( 9 / 24 )3052.8703703703796.930868786764831.4953369198236
Trimmed Mean ( 10 / 24 )3048.3076923076995.830101742857431.8095007400417
Trimmed Mean ( 11 / 24 )3044.7694.901291619347332.0834411001765
Trimmed Mean ( 12 / 24 )3039.87593.876808446000632.3815333128691
Trimmed Mean ( 13 / 24 )3035.3478260869692.936850501049432.6603259064894
Trimmed Mean ( 14 / 24 )3029.7954545454591.979192538229132.9400092666196
Trimmed Mean ( 15 / 24 )3023.8333333333390.70891221765633.3355704462385
Trimmed Mean ( 16 / 24 )3018.4590.363553110583433.4034009962638
Trimmed Mean ( 17 / 24 )3009.9210526315890.812653049461533.1442915888848
Trimmed Mean ( 18 / 24 )3000.9444444444491.244821070206732.8889290290286
Trimmed Mean ( 19 / 24 )2991.4705882352991.799928109344332.5868510994051
Trimmed Mean ( 20 / 24 )2980.7812592.161266599585732.3431020425385
Trimmed Mean ( 21 / 24 )2969.1333333333392.304851410257632.1666010829349
Trimmed Mean ( 22 / 24 )2956.3571428571492.435838097444831.9828023816973
Trimmed Mean ( 23 / 24 )2941.8461538461592.172375175874331.9167879555323
Trimmed Mean ( 24 / 24 )2924.3333333333391.129619158222732.0898228297871
Median2679
Midrange3183.5
Midmean - Weighted Average at Xnp2985.97297297297
Midmean - Weighted Average at X(n+1)p3000.94444444444
Midmean - Empirical Distribution Function2985.97297297297
Midmean - Empirical Distribution Function - Averaging3000.94444444444
Midmean - Empirical Distribution Function - Interpolation3000.94444444444
Midmean - Closest Observation2985.97297297297
Midmean - True Basic - Statistics Graphics Toolkit3000.94444444444
Midmean - MS Excel (old versions)3009.92105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3091.72222222222 & 106.105860016405 & 29.1380911642789 \tabularnewline
Geometric Mean & 2963.34985769817 &  &  \tabularnewline
Harmonic Mean & 2840.34310390148 &  &  \tabularnewline
Quadratic Mean & 3218.39967996518 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 3092.625 & 105.533413775553 & 29.3046997093959 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 3093.23611111111 & 105.122220939777 & 29.4251404075946 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 3092.11111111111 & 104.883068051199 & 29.4815089657913 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 3091.05555555556 & 103.863679332776 & 29.7606976318632 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 3094.52777777778 & 101.914989529773 & 30.363813920363 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 3095.11111111111 & 101.577372769077 & 30.4704780871567 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 3088.20833333333 & 100.095206903384 & 30.8527094240805 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 3082.65277777778 & 98.7228165468023 & 31.2253325584199 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 3082.52777777778 & 98.5410175955005 & 31.281671866138 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 3072.94444444444 & 96.0844777973383 & 31.9816948053348 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 3080.58333333333 & 94.8385184478182 & 32.4824067662795 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 3074.58333333333 & 92.5806689440529 & 33.2097766024063 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 3079.45833333333 & 90.7105793649482 & 33.9481718107434 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 3078.48611111111 & 90.1495041354895 & 34.1486749220975 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 3068.69444444444 & 83.2912209059483 & 36.8429518869652 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 3090.47222222222 & 77.3815162048741 & 39.938119253698 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 3086.22222222222 & 76.4918046236218 & 40.3470964949512 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 3081.47222222222 & 74.7938977519691 & 41.199513795109 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 3081.73611111111 & 74.4852076802319 & 41.373800343568 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 3077.84722222222 & 73.915920119773 & 41.6398418261572 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 3073.47222222222 & 72.0614928573201 & 42.6506876329584 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 3071.63888888889 & 71.3211682443033 & 43.0677029625665 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 3076.11111111111 & 70.8089644785909 & 43.442396506747 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 3050.11111111111 & 66.9266309197893 & 45.5739526880807 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 3089.1 & 104.707541338962 & 29.5021730096772 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 3085.36764705882 & 103.678309173045 & 29.7590467250886 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 3081.07575757576 & 102.658133883765 & 30.0129725820296 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 3076.9375 & 101.492485635031 & 30.3168996280644 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 3072.83870967742 & 100.401610766458 & 30.6054722251924 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 3067.63333333333 & 99.6059183192367 & 30.7977014327761 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 3061.94827586207 & 98.6498247050947 & 31.0385576965342 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 3057.125 & 97.7744391427295 & 31.267118756235 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 3052.87037037037 & 96.9308687867648 & 31.4953369198236 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 3048.30769230769 & 95.8301017428574 & 31.8095007400417 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 3044.76 & 94.9012916193473 & 32.0834411001765 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 3039.875 & 93.8768084460006 & 32.3815333128691 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 3035.34782608696 & 92.9368505010494 & 32.6603259064894 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 3029.79545454545 & 91.9791925382291 & 32.9400092666196 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 3023.83333333333 & 90.708912217656 & 33.3355704462385 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 3018.45 & 90.3635531105834 & 33.4034009962638 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 3009.92105263158 & 90.8126530494615 & 33.1442915888848 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 3000.94444444444 & 91.2448210702067 & 32.8889290290286 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2991.47058823529 & 91.7999281093443 & 32.5868510994051 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2980.78125 & 92.1612665995857 & 32.3431020425385 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2969.13333333333 & 92.3048514102576 & 32.1666010829349 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2956.35714285714 & 92.4358380974448 & 31.9828023816973 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2941.84615384615 & 92.1723751758743 & 31.9167879555323 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2924.33333333333 & 91.1296191582227 & 32.0898228297871 \tabularnewline
Median & 2679 &  &  \tabularnewline
Midrange & 3183.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2985.97297297297 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3000.94444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2985.97297297297 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3000.94444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3000.94444444444 &  &  \tabularnewline
Midmean - Closest Observation & 2985.97297297297 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3000.94444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3009.92105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=177542&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]3091.72222222222[/C][C]106.105860016405[/C][C]29.1380911642789[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2963.34985769817[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2840.34310390148[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3218.39967996518[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]3092.625[/C][C]105.533413775553[/C][C]29.3046997093959[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]3093.23611111111[/C][C]105.122220939777[/C][C]29.4251404075946[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]3092.11111111111[/C][C]104.883068051199[/C][C]29.4815089657913[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]3091.05555555556[/C][C]103.863679332776[/C][C]29.7606976318632[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]3094.52777777778[/C][C]101.914989529773[/C][C]30.363813920363[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]3095.11111111111[/C][C]101.577372769077[/C][C]30.4704780871567[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]3088.20833333333[/C][C]100.095206903384[/C][C]30.8527094240805[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]3082.65277777778[/C][C]98.7228165468023[/C][C]31.2253325584199[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]3082.52777777778[/C][C]98.5410175955005[/C][C]31.281671866138[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]3072.94444444444[/C][C]96.0844777973383[/C][C]31.9816948053348[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]3080.58333333333[/C][C]94.8385184478182[/C][C]32.4824067662795[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]3074.58333333333[/C][C]92.5806689440529[/C][C]33.2097766024063[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]3079.45833333333[/C][C]90.7105793649482[/C][C]33.9481718107434[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]3078.48611111111[/C][C]90.1495041354895[/C][C]34.1486749220975[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]3068.69444444444[/C][C]83.2912209059483[/C][C]36.8429518869652[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]3090.47222222222[/C][C]77.3815162048741[/C][C]39.938119253698[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]3086.22222222222[/C][C]76.4918046236218[/C][C]40.3470964949512[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]3081.47222222222[/C][C]74.7938977519691[/C][C]41.199513795109[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]3081.73611111111[/C][C]74.4852076802319[/C][C]41.373800343568[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]3077.84722222222[/C][C]73.915920119773[/C][C]41.6398418261572[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]3073.47222222222[/C][C]72.0614928573201[/C][C]42.6506876329584[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]3071.63888888889[/C][C]71.3211682443033[/C][C]43.0677029625665[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]3076.11111111111[/C][C]70.8089644785909[/C][C]43.442396506747[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]3050.11111111111[/C][C]66.9266309197893[/C][C]45.5739526880807[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]3089.1[/C][C]104.707541338962[/C][C]29.5021730096772[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]3085.36764705882[/C][C]103.678309173045[/C][C]29.7590467250886[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]3081.07575757576[/C][C]102.658133883765[/C][C]30.0129725820296[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]3076.9375[/C][C]101.492485635031[/C][C]30.3168996280644[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]3072.83870967742[/C][C]100.401610766458[/C][C]30.6054722251924[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]3067.63333333333[/C][C]99.6059183192367[/C][C]30.7977014327761[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]3061.94827586207[/C][C]98.6498247050947[/C][C]31.0385576965342[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]3057.125[/C][C]97.7744391427295[/C][C]31.267118756235[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]3052.87037037037[/C][C]96.9308687867648[/C][C]31.4953369198236[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]3048.30769230769[/C][C]95.8301017428574[/C][C]31.8095007400417[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]3044.76[/C][C]94.9012916193473[/C][C]32.0834411001765[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]3039.875[/C][C]93.8768084460006[/C][C]32.3815333128691[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]3035.34782608696[/C][C]92.9368505010494[/C][C]32.6603259064894[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]3029.79545454545[/C][C]91.9791925382291[/C][C]32.9400092666196[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]3023.83333333333[/C][C]90.708912217656[/C][C]33.3355704462385[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]3018.45[/C][C]90.3635531105834[/C][C]33.4034009962638[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]3009.92105263158[/C][C]90.8126530494615[/C][C]33.1442915888848[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]3000.94444444444[/C][C]91.2448210702067[/C][C]32.8889290290286[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2991.47058823529[/C][C]91.7999281093443[/C][C]32.5868510994051[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2980.78125[/C][C]92.1612665995857[/C][C]32.3431020425385[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2969.13333333333[/C][C]92.3048514102576[/C][C]32.1666010829349[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2956.35714285714[/C][C]92.4358380974448[/C][C]31.9828023816973[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2941.84615384615[/C][C]92.1723751758743[/C][C]31.9167879555323[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2924.33333333333[/C][C]91.1296191582227[/C][C]32.0898228297871[/C][/ROW]
[ROW][C]Median[/C][C]2679[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3183.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2985.97297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3000.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2985.97297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3000.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3000.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2985.97297297297[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3000.94444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3009.92105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=177542&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=177542&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3091.72222222222106.10586001640529.1380911642789
Geometric Mean2963.34985769817
Harmonic Mean2840.34310390148
Quadratic Mean3218.39967996518
Winsorized Mean ( 1 / 24 )3092.625105.53341377555329.3046997093959
Winsorized Mean ( 2 / 24 )3093.23611111111105.12222093977729.4251404075946
Winsorized Mean ( 3 / 24 )3092.11111111111104.88306805119929.4815089657913
Winsorized Mean ( 4 / 24 )3091.05555555556103.86367933277629.7606976318632
Winsorized Mean ( 5 / 24 )3094.52777777778101.91498952977330.363813920363
Winsorized Mean ( 6 / 24 )3095.11111111111101.57737276907730.4704780871567
Winsorized Mean ( 7 / 24 )3088.20833333333100.09520690338430.8527094240805
Winsorized Mean ( 8 / 24 )3082.6527777777898.722816546802331.2253325584199
Winsorized Mean ( 9 / 24 )3082.5277777777898.541017595500531.281671866138
Winsorized Mean ( 10 / 24 )3072.9444444444496.084477797338331.9816948053348
Winsorized Mean ( 11 / 24 )3080.5833333333394.838518447818232.4824067662795
Winsorized Mean ( 12 / 24 )3074.5833333333392.580668944052933.2097766024063
Winsorized Mean ( 13 / 24 )3079.4583333333390.710579364948233.9481718107434
Winsorized Mean ( 14 / 24 )3078.4861111111190.149504135489534.1486749220975
Winsorized Mean ( 15 / 24 )3068.6944444444483.291220905948336.8429518869652
Winsorized Mean ( 16 / 24 )3090.4722222222277.381516204874139.938119253698
Winsorized Mean ( 17 / 24 )3086.2222222222276.491804623621840.3470964949512
Winsorized Mean ( 18 / 24 )3081.4722222222274.793897751969141.199513795109
Winsorized Mean ( 19 / 24 )3081.7361111111174.485207680231941.373800343568
Winsorized Mean ( 20 / 24 )3077.8472222222273.91592011977341.6398418261572
Winsorized Mean ( 21 / 24 )3073.4722222222272.061492857320142.6506876329584
Winsorized Mean ( 22 / 24 )3071.6388888888971.321168244303343.0677029625665
Winsorized Mean ( 23 / 24 )3076.1111111111170.808964478590943.442396506747
Winsorized Mean ( 24 / 24 )3050.1111111111166.926630919789345.5739526880807
Trimmed Mean ( 1 / 24 )3089.1104.70754133896229.5021730096772
Trimmed Mean ( 2 / 24 )3085.36764705882103.67830917304529.7590467250886
Trimmed Mean ( 3 / 24 )3081.07575757576102.65813388376530.0129725820296
Trimmed Mean ( 4 / 24 )3076.9375101.49248563503130.3168996280644
Trimmed Mean ( 5 / 24 )3072.83870967742100.40161076645830.6054722251924
Trimmed Mean ( 6 / 24 )3067.6333333333399.605918319236730.7977014327761
Trimmed Mean ( 7 / 24 )3061.9482758620798.649824705094731.0385576965342
Trimmed Mean ( 8 / 24 )3057.12597.774439142729531.267118756235
Trimmed Mean ( 9 / 24 )3052.8703703703796.930868786764831.4953369198236
Trimmed Mean ( 10 / 24 )3048.3076923076995.830101742857431.8095007400417
Trimmed Mean ( 11 / 24 )3044.7694.901291619347332.0834411001765
Trimmed Mean ( 12 / 24 )3039.87593.876808446000632.3815333128691
Trimmed Mean ( 13 / 24 )3035.3478260869692.936850501049432.6603259064894
Trimmed Mean ( 14 / 24 )3029.7954545454591.979192538229132.9400092666196
Trimmed Mean ( 15 / 24 )3023.8333333333390.70891221765633.3355704462385
Trimmed Mean ( 16 / 24 )3018.4590.363553110583433.4034009962638
Trimmed Mean ( 17 / 24 )3009.9210526315890.812653049461533.1442915888848
Trimmed Mean ( 18 / 24 )3000.9444444444491.244821070206732.8889290290286
Trimmed Mean ( 19 / 24 )2991.4705882352991.799928109344332.5868510994051
Trimmed Mean ( 20 / 24 )2980.7812592.161266599585732.3431020425385
Trimmed Mean ( 21 / 24 )2969.1333333333392.304851410257632.1666010829349
Trimmed Mean ( 22 / 24 )2956.3571428571492.435838097444831.9828023816973
Trimmed Mean ( 23 / 24 )2941.8461538461592.172375175874331.9167879555323
Trimmed Mean ( 24 / 24 )2924.3333333333391.129619158222732.0898228297871
Median2679
Midrange3183.5
Midmean - Weighted Average at Xnp2985.97297297297
Midmean - Weighted Average at X(n+1)p3000.94444444444
Midmean - Empirical Distribution Function2985.97297297297
Midmean - Empirical Distribution Function - Averaging3000.94444444444
Midmean - Empirical Distribution Function - Interpolation3000.94444444444
Midmean - Closest Observation2985.97297297297
Midmean - True Basic - Statistics Graphics Toolkit3000.94444444444
Midmean - MS Excel (old versions)3009.92105263158
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')